I need to create a table showing the probability of ten possibilities. I need to know the probability of rolling two 10-sided dice, however my criteria aren't like the formulas easily to found on Google;
In every case, the first die MUST be the roll of a 10 on a 10-sided die.
The second die must roll a specific number, OR higher.
In the first entry, the second die must roll 10 also, so the chance is 10 x 10, or 1 in 100, easy enough.
In the last entry, the second die must roll any number 1 through 10, so the second die can be discounted and the odds are simply 1 in 10.
The rest, I'm not entirely certain of. The second die in the second entry must roll either 9 OR 10. The third entry must roll either a 8 OR 9 OR 10. Etc.
Table
First Die - Second Die - (Outcome)
10 - 10 - (1 in 100)
10 - 9 or 10
10 - 8 or 9 or 10
10 - 7 or 8 or 9 or 10
10 - 6 or 7 or 8 or 9 or 10
10 - 5 or 6 or 7 or 8 or 9 or 10
10 - 4 or 5 or 6 or 7 or 8 or 9 or 10
10 - 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10
10 - 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10
10 - 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10 - (1 in 10)
It seems logical that as the second die requires less numbers to reach its potential out of the possibilities, that the odds would decrease incrementally by 10%, so the first entry is 1 in 100, the second would be 1 in 90, then 1 in 80, 1 in 70, etc. all the way down to 1 in 10, but I'm merely hypothesizing based on the first and last entries and what I know of odds of rolling the same number of two or more different dice. This formula tweaks my brain because its not rolling the same number on both die, but a specific number on the first die, and a variable rate OR higher on the second die. It seems odd to me that using this method shows the odds of rolling a 10 on one die AND a 5-10 on the second die has a 1 in 50 chance of success.
In every case, the first die MUST be the roll of a 10 on a 10-sided die.
The second die must roll a specific number, OR higher.
In the first entry, the second die must roll 10 also, so the chance is 10 x 10, or 1 in 100, easy enough.
In the last entry, the second die must roll any number 1 through 10, so the second die can be discounted and the odds are simply 1 in 10.
The rest, I'm not entirely certain of. The second die in the second entry must roll either 9 OR 10. The third entry must roll either a 8 OR 9 OR 10. Etc.
Table
First Die - Second Die - (Outcome)
10 - 10 - (1 in 100)
10 - 9 or 10
10 - 8 or 9 or 10
10 - 7 or 8 or 9 or 10
10 - 6 or 7 or 8 or 9 or 10
10 - 5 or 6 or 7 or 8 or 9 or 10
10 - 4 or 5 or 6 or 7 or 8 or 9 or 10
10 - 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10
10 - 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10
10 - 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9 or 10 - (1 in 10)
It seems logical that as the second die requires less numbers to reach its potential out of the possibilities, that the odds would decrease incrementally by 10%, so the first entry is 1 in 100, the second would be 1 in 90, then 1 in 80, 1 in 70, etc. all the way down to 1 in 10, but I'm merely hypothesizing based on the first and last entries and what I know of odds of rolling the same number of two or more different dice. This formula tweaks my brain because its not rolling the same number on both die, but a specific number on the first die, and a variable rate OR higher on the second die. It seems odd to me that using this method shows the odds of rolling a 10 on one die AND a 5-10 on the second die has a 1 in 50 chance of success.
"The true value of a human being is determined primarily by the measure and the sense in which he has attained liberation from the self." -Albert Einsetin